Abstract : The present study considers the identification of crystal plasticity parameters from the knowledge of a deformed microstructure, which has been backtracked to the reference state, and known kinematics along the sample surface. This theoretical question is tackled on a numerical (synthetic) test case. A 2D microstructure with one dimension along the depth is generated, and deformed using known crystal plasticity law. A procedure is proposed to perform the calibration of the constitutive parameters addressing the specific challenge of having a partial knowledge of the boundary conditions. The proposed identification strategy combined with the estimation of the reference microstructure is shown to retrieve the constitutive parameters with good accuracy.